Abstract :
For long memory time series models with uncorrelated but dependent errors, we
establish the asymptotic normality of the Whittle estimator under mild conditions.
Our framework includes the widely used fractional autoregressive integrated moving
average models with generalized autoregressive conditional heteroskedastic-type innovations.
To cover nonstationary fractionally integrated processes, we extend the
idea of Abadir, Distaso, and Giraitis (2007, Journal of Econometrics 141, 1353–
1384) and develop the nonstationarity-extended Whittle estimation. The resulting
estimator is shown to be asymptotically normal and is more efficient than the tapered
Whittle estimator. Finally, the results from a small simulation study are presented to
corroborate our theoretical findings.
